(9x+5)(6x+8)=0

Solution for (9x+5)(6x+8)=0 equation:

(9x+5)(6x+8)=0

We multiply parentheses ..

(+54x^2+72x+30x+40)=0

We get rid of parentheses

54x^2+72x+30x+40=0

We add all the numbers together, and all the variables

54x^2+102x+40=0

a = 54; b = 102; c = +40;
Δ = b2-4ac
Δ = 1022-4·54·40
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-42}{2*54}=\frac{-144}{108}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+42}{2*54}=\frac{-60}{108}
=-5/9
$